Inclusion problems in ordered topological vector spaces and applications
type: Item
instance of: scholarly article
title: Inclusion problems in ordered topological vector spaces and applications
zbMATH Open document ID: 1070.47051
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-11-23T00:00:00Z
review text: The author studies the existence of minimal and maximal solutions of inclusion problems in ordered topological vector spaces (TVS) of the form \(Lu\in Nu\) where \(L\) is a single-valued map from a partially ordered set \(V\) onto a nonempty subset \(P\) of an ordered TVS \(X\) (satisfying some order-theoretic assumptions) and \(N\) is a set-valued map on \(V\) admitting nonempty values in \(X\). The obtained results are then applied to some more concrete problems in reflexive lattice-ordered Banach spaces and, in particular, to some functional parabolic initial-boundary and elliptic boundary value problems for partial differential inclusions in order to get minimal and maximal weak solutions with respect to the natural almost everywhere pointwise order that is introduced in appropriate Sobolev-type spaces.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 2117729
zbMATH Keywords: ordered space
zbMATH Keywords: minimal solution
zbMATH Keywords: partial differential inclusion
author: S. Heikkilä
reviewed by: Wojciech Kryszewski
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.03.074
OpenAlex ID: W1966209477
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DOI: 10.1016/J.JMAA.2004.03.074
description: scientific article; zbMATH DE number 2117729